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Proof step 67 from proof inv-commit (previous step)

# lpt1 = # lpt, # avol = # lpt, # lpt0 = # lpt, # lpt2 = # lpt, keyset(gch1) = gc-heap(cleanup-lpt(lpt), []), keyset(gch0) = gc-heap(lpt2, []), keyset(gch) = gc-heap(lpt2, log1), avol-cleanup-lpt-unchanged(avol, avol0, lpt), awbuf-inv(avol0, nobuffer), awbuf-inv(avol, nobuffer), awbuf-inv(avol, bleb0), bin-heap-inv(gch1, lpt1), bin-heap-inv(gch0, lpt), bin-heap-inv(gch, lpt2), buf-ro-rw-mode(false, bleb0, lpt2, avol), bufs-log-only(bleb0, log1, lpt2), freelist-cons(cleanup-lpt(lpt), freelist0), freelist-cons(lpt2, freelist), id-idx(lpt2, lpt), log-group-block(log1, lpt2), lpt-free-unref(lpt0), lpt-free-unref(lpt2), lpt-leb-size(lpt0), lpt-leb-size(lpt2), lpt-ram-flash(lpt2, lpt0, log1), lpt-ram-flash(lpt, lpt2, []), synced(avol0), synced(avol), ∀ n. n ∈ log1 → n < # lpt ∧ lpt2[n].flags = LP_GROUP_NODES, ∀ n. n < # lpt → cleanup-lpt(lpt)[n].ref-size = lpt1[n].ref-size ∧ cleanup-lpt(lpt)[n].size = lpt1[n].size ∧ cleanup-lpt(lpt)[n].flags = lpt1[n].flags ⊦ dups(log1), lpt-leb-size(cleanup-lpt(lpt)) ∧ # lpt = # avol0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 68:
⊦ avol-cleanup-lpt-unchanged(avol0, avol1, lpt) ↔ # avol0 = # avol1 ∧ # avol0 = # lpt ∧ (∀ n. n < # avol0 ∧ (lpt[n].ref-size ≠ 0 ∨ lpt[n].flags = LP_FREE) → avol0[n] = avol1[n])
Proof step 69:
# avol = # avol0, # lpt2 = # lpt, # lpt0 = # lpt, # avol = # lpt, # lpt1 = # lpt, keyset(gch) = gc-heap(lpt2, log1), keyset(gch0) = gc-heap(lpt2, []), keyset(gch1) = gc-heap(cleanup-lpt(lpt), []), awbuf-inv(avol, bleb0), awbuf-inv(avol, nobuffer), awbuf-inv(avol0, nobuffer), bin-heap-inv(gch, lpt2), bin-heap-inv(gch0, lpt), bin-heap-inv(gch1, lpt1), buf-ro-rw-mode(false, bleb0, lpt2, avol), bufs-log-only(bleb0, log1, lpt2), freelist-cons(lpt2, freelist), freelist-cons(cleanup-lpt(lpt), freelist0), id-idx(lpt2, lpt), log-group-block(log1, lpt2), lpt-free-unref(lpt2), lpt-free-unref(lpt0), lpt-leb-size(lpt2), lpt-leb-size(lpt0), lpt-ram-flash(lpt, lpt2, []), lpt-ram-flash(lpt2, lpt0, log1), synced(avol), synced(avol0), ∀ n. n < # lpt → cleanup-lpt(lpt)[n].ref-size = lpt1[n].ref-size ∧ cleanup-lpt(lpt)[n].size = lpt1[n].size ∧ cleanup-lpt(lpt)[n].flags = lpt1[n].flags, ∀ n. n ∈ log1 → n < # lpt ∧ lpt2[n].flags = LP_GROUP_NODES, ∀ n. n < # avol ∧ (lpt[n].ref-size ≠ 0 ∨ lpt[n].flags = LP_FREE) → avol[n] = avol0[n] ⊦ dups(log1), lpt-leb-size(cleanup-lpt(lpt)) ∧ # lpt = # avol0

Rule argument

spec: persistence-base name: avol-cleanup-lpt-unchanged seq: ⊦ avol-cleanup-lpt-unchanged(avol0, avol1, lpt) ↔ # avol0 = # avol1 ∧ # avol0 = # lpt ∧ (∀ n. n < # avol0 ∧ (lpt[n].ref-size ≠ 0 ∨ lpt[n].flags = LP_FREE) → avol0[n] = avol1[n]) subst: [lpt, avol1, avol0] → [lpt, avol0, avol] flags: <all paths>

Additional information

Used terms: lpt, avol0, avol